Golden Mean and the pentagon_
Stonemasonry technical skills
atSkillsTech Australia
Method
•Construct a double square rectangle side: length = 1 : 2 [100mm : 200mm]
•Using Pythagoras’ Theorem, prove that its diagonal has a length equivalent to [224mm]
•Use the half diagonal to produce a Golden Rectangle side: length = 1: = 1: φ [100mm: 162mm]
•Discuss the Golden Mean (a+b): a = a: b
•Use the half diagonal to inscribe a pentagon in a circle with radius = 1.
Golden Mean and the Pentagon
2
15
2
5
Step 1: Draw vertical and horizontal centerlines at page centre right, intersecting at point A
Step 2: Construct a circle centred at A with radius 1 [1 x 100mm]
Step 3: Construct a double square with side 1 [1 x 100mm]
Step 4: Join the diagonal of the double square from top right to bottom left, intersecting the horizontal line at point B
Step 5: Centre compasses at point B and with radius BC = scribe semicircular arc BDE
2
5
Step 6: Centre compasses at point C and with radius CE scribe an arc to intersect the circle at point F
Step 7: Step off CF around the circle and join the points to form a pentagon
Step 8: Construct the Golden Rectangle AC : AD = 1: so that (a+b) : a = a : b
2
15